Bring a pot of salted water to a boil and prepare an ice bath.
Once the water is boiling, add the herbs and cook for about 10 to 15 seconds; just until the herbs/stems are bright green.
Using a slotted spoon, quickly transfer to the ice bath and let sit for 5 minutes to completely cool.
Transfer the herbs to a dry tea towel and wrap/dry. The goal is to get as much moisture out of the herbs.
Transfer the herbs to a high-speed blender and add the oil. Puree until as smooth as can be. This can work with a regular blender, but it’s not quite as effective.
If the mixture feels too thick to blend, add a bit more oil.
Line a sieve with cheesecloth (layered three times) or a coffee filter. Pour the oil into the sieve and let sit for a few hours, stirring occasionally. Do not press the oil through.
Once done, transfer to a bottle and store in the refrigerator for up to a week (sometimes a little longer- keep an eye on it!).